Madrid: Injured last month in a Copa del Rey game against Getafe, the Brazilian began training earlier this week and is available for selection against Rayo Vallecano on Saturday.
The 22-year-old has missed a total of eight games through injury, but Barcelona coach Gerardo Martino said at a press conference on Friday that he is ready for first-team action again.
"He has trained very well and recovered very well as we have seen in training," he said. "Obviously, it remains to be seen how he responds on the pitch."
A final decision on his participation will be taken on Saturday for the game against second-bottom Rayo at the Camp Nou.
His return should boost Barcelona, who are top of La Liga, as they enter a crucial phase of the season.
Martino said Saturday's clash against the side from Madrid would be a "very difficult match which we have to win to remain top of the league".
Barcelona head La Liga, but going into this weekend's round of fixtures they are tied on 57 points with arch-rivals Real Madrid as well as Atletico Madrid.
Barcelona face City in England on Tuesday, February 18, in the first leg of the last 16 of the Champions League.
Neymar has scored six times in La Liga since his controversial transfer from Santos last summer, which is being investigated for irregularities by the Brazilian and Spanish authorities.